Molecular field theory, the onsager reaction field, and the spherical model

Abstract

We have extended the Onsager method of solution of the many-dipole problem to other types of interaction, particularly to the Ising model, and to the presence of long-range order. We demonstrate that the use of linear response theory for the calculation of reaction field and cavity field is justified on account of the fluctuation theorem. In the paramagnetic phase, the Onsager method reduces to the spherical model. In the magnetized phase, we introduce a scheme of successive approximations and recover the Weiss theory and the modified spherical model after the first and second iterations, respectively. © 1968 The American Institute of Physics.